First of all, that's not the way the story goes. This is the way it goes:

A poor couple longs for a child, and finally the wife becomes pregnant. Unfortunately, she then happens to look out her window one day and sees a bed of rampion/rapunzel growing in the next door neighbour's garden. The next door neighbour is a witch/sorceress. The wife develops a craving for the rampion, so the husband (eventually) goes and steals some for her. The witch catches the husband the second time he steals rampion, and in payment for the stolen rampion, the couple must give up the child the wife is pregnant with. The baby is named Rapunzel for this reason. When Rapunzel turns 12, the witch/adoptive mother locks her up in the tower, until one day a prince comes by. Rapunzel lets him climb up her hair, they talk, they get engaged, ect. But the witch finds out about this, and takes Rapunzel to a desert/forest and leaves her there. She also blinds the prince. Eventually, the blind prince finds Rapunzel again, and Rapunzel heals his eyesight with her magical tears.

In the original German Rapunzel version of the story, Rapunzel gives birth to twins while in the desert/forest, but this is often edited out because of *gasp* implied premarital sex.

The first literary version was Italian, written by GiambattistaBasile in 1637. The story was titled "Pentamerone". The girl was named Petrosinella, after "petrosine", or parsley.

Sixty years later in 1697, CharlotteRose de Caumont de la Force, a French aristocrat, published her own version of the tale, titled "Persinette". This time the girl is named Persinette, French for "parsley".

"Persinette" was translated into German several times. One translation by J. C. F. Schulz is thought to be the indirect source of the Grimms' tale. Schulz was responsible for changing the parsley into rampion/rapunzel. The Grimms were apparently unaware of the literary tales of La Force and Schulz, and assumed the tale was oral in origin (they only collected oral stories, they didn't retell published stories).

Rampion/rapunzel is a real plant. In Latin it's called "Campanula rapunculus", and it has blue bell-shaped flowers and roots that are indeed edible. From Dictionary.com (feel free to dispute this!), it says the word rampion ultimately derives from Latin, "turnip". I believe "rapunzel" is the German version of "rampion", so that explains Rapunzel's name in German/Schulz/Grimms' version.